
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
JaeDong Lee, Kenneth E. Batcher, "Minimizing Communication in the Bitonic Sort," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 5, pp. 459474, May, 2000.  
BibTex  x  
@article{ 10.1109/71.852399, author = {JaeDong Lee and Kenneth E. Batcher}, title = {Minimizing Communication in the Bitonic Sort}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {11}, number = {5}, issn = {10459219}, year = {2000}, pages = {459474}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.852399}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Minimizing Communication in the Bitonic Sort IS  5 SN  10459219 SP459 EP474 EPD  459474 A1  JaeDong Lee, A1  Kenneth E. Batcher, PY  2000 KW  Bitonic sorting KW  parallel computing KW  sorting networks KW  omega networks KW  sorting KW  minimizing communication. VL  11 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Abstract—This paper presents bitonic sorting schemes for specialpurpose parallel architectures such as sorting networks and for generalpurpose parallel architectures such as SIMD and/or MIMD computers. First, bitonic sorting algorithms for sharedmemory SIMD and/or MIMD computers are developed. Sharedmemory accesses through the interconnection network of shared memory SIMD and/or MIMD computers can be very time consuming. A scheme is introduced which reduces the number of such accesses. This scheme is based on the
[1] M. Ajtai,J. Komlos,W.L. Steiger, and E. Szemeredi,"An O(n log n) sorting network," Proc. Ann. ACM Symp. Theory of Computing, pp. 19, 1983.
[2] S.G. Akl, Parallel Sorting Algorithms.Orlando, Fla.: Academic Press Inc., 1985.
[3] K.E. Batcher, “On Bitonic Sorting Networks,” Proc. 1990 Int'l Conf. Parallel Processing, 1990.
[4] K.E. Batcher, “Sorting Networks and Their Applications,” Proc. Spring Joint Computer Conf., AFIPS, vol. 32, pp. 307314, 1968.
[5] G.M. Baudet and D. Stevenson, “Optimal Sorting Algorithms for Parallel Computers,” IEEE Trans. Computers, vol. 27, no. 1, pp. 8487, Jan. 1978.
[6] M. Chien and A. Oru, ”Adaptive Binary Sorting Schemes and Associated Interconnection Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 6, June 1994.
[7] S. Fineberg, T. Casavant, and H.J. Siegel, ”Experimental Analysis of a MixedMode Parallel Architecture Using Bitonic Sequence Sorting,” J. Parallel and Distributed Computing, vol. 11, pp. 139251, Mar. 1991.
[8] M. Flynn, “Very HighSpeed Computing Systems,” Proc. IEEE, vol. 54, pp. 1,9011,909, Dec. 1966.
[9] A. Gottlieb, R. Grishman, C. Kruskal, K. McAuliffe, L. Rudolph, and M. Snir, ”The NYU Ultracomputer—Designing an MIMD Shared Memory Parallel Computer,” IEEE Trans. Computers, vol. 32, no. 2, pp. 175189, Feb. 1983.
[10] K. Hwang, Advanced Computer Architecture: Parallelism, Scalability, Programmability. McGrawHill, 1993.
[11] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. AddisonWesley, 1973.
[12] M. Kumar and D. Hirschberg, ”An Efficient Implementation of Batcher's OddEven Merge Algorithm and Its Application in Parallel Sorting Schemes,” IEEE Trans. Computers, vol. 32, no. 3, pp. 254264, Mar. 1983.
[13] V. Kumar, A. Grama, A. Gupta, and G. Karypis, Introduction to Parallel Computing: Design and Analysis of Algorithms. Benjamin Cummings, 1994.
[14] D. Lawrie, ”Access and Alignment of Data in an Array Processor,” IEEE Trans. Computers, vol. 24, no. 12, pp. 1,1451,155, Dec. 1975.
[15] J.D. Lee, ”Design of GeneralPurpose Bitonic Sorting Algorithms with a Fixed Number of Processors for SharedMemory Parallel Computers,” J. KISS(A): Computer Systems and Theory, vol. 26, no. 1, pp. 3342, 1999.
[16] J.D. Lee and K.E. Batcher, ”Simplifying Multistage Hardware Interconnection in the Bitonic Sorting Network” Proc. Seventh IASTED/ISMM Int'l Conf. Parallel and Distributed Computing and Systems, pp. 138142, 1995.
[17] J.D. Lee and K.E. Batcher, ”A Bitonic Sorting Network with Simpler FlipInterconnections,” Proc. ISPAN '96: Int'l Symp. Parallel Architectures, Algorithms, and Networks, pp. 104109, 1996.
[18] J.D. Lee and K.E. Batcher, ”Minimizing Communication of a Recirculating Bitonic Sorting Network,” Proc. 25th Int'l Conf. Parallel Processing, vol. I, pp. I251254, 1996.
[19] T. Leighton, "Tight Bounds on the Complexity of Parallel Sorting," IEEE Trans. Computers, vol. 34, no. 4, pp. 344354, Apr. 1985.
[20] K. Liszka, ”Generalized Bitonic and OddEven Merging Networks,” doctoral dissertation, Dept. of Math. and Computer Science, Kent State Univ., 1992.
[21] D. Nassimi and S. Sahni, ”Bitonic Sort on a MeshConnected Parallel Computer,” IEEE Trans. Computers, vol. 27, no. 1, pp. 27, Jan. 1979.
[22] T. Nakatani, S.T. Huang, B.W. Arden, and S.K. Tripathi, "KWay Bitonic Sort," IEEE Trans. Computers, vol. 38, no. 2, pp. 283288, Feb. 1989.
[23] S. Orcutt, ”Implementation of Permutation Functions in ILLIAC IV Type Computers,” IEEE Trans. Computers, vol. 25, no. 9, pp. 929936, 1976.
[24] M.S. Paterson, ”Improved Sorting Networks with$O(\log N)$Depth,” Algorithmica, vol. 5, pp. 7592, 1990.
[25] M.J. Quinn, Parallel Computing: Theory and Practice.New York: McGrawHill, 1994.
[26] H.J. Siegel, Interconnection Networks for LargeScale Parallel Processing, Second Ed., McGrawHill, New York, 1990.
[27] H. Siegel, ”The Universality of Various Types of SIMD Machine Interconnection Networks,” Proc. Fourth Ann. Symp. Computer Architecture, pp. 2325, 1977.
[28] H.S. Stone, ”Parallel Processing with the Perfect Shuffle,” IEEE Trans. Computers, vol. 20, pp. 153161, Feb. 1971.
[29] C. Thompson and H. Kung,“Sorting on a mesh connected parallel computer,”Commun. ACM, vol. 20, pp. 263–271, 1977.
[30] B. Wang, G. Chen, and C. Hsu, ”Bitonic Sort with an Arbitrary Number of Keys,” Proc. 1991 Int'l Conf. Parallel Processing, vol. 3, pp. 5861, 1991.